Adaptive Autobalancing Boundary Control
for a Flexible Rotor

Abstract:

In this project, we design a control strategy for a spinning
rotor with an unbalanced disk attached to its free end. The control
strategy is composed of a boundary torque applied to the clamped
end, and two boundary forces and two boundary torques applied to
the free-end. At the clamped-end, the boundary torque ensures that
the rotor tracks a desired angular velocity trajectory, while at
the free-end, the boundary forces and torques ensure that the rotor
displacement is regulated at every point along the length of the
rotor. Under the assumption of exact model knowledge, we first
develop a model-based control law which exponentially achieves the
control objectives. We then illustrate how the model-based control
law can be redesigned as an adaptive controller which
asymptotically achieves the same control objectives while
compensating for parameteric uncertainty associated with unbalanced
operation. Simulation results illustrate controller
performance.

Theory

Over the last decade, the study of the effects of flexiblility
on lightweight body-beam systems has been propelled into the
limelight. Motivated, for example, by the prohibitive cost of
placing equipment in space, many structural designers and control
researchers have focused on lightweight mechanical systems with
rigid and flexible components. Mathemtically, such systems are
often characterized by a combination of ordinary differential
equations (ODEs), partial differentialk equations (PDEs), and a set
of boundary conditions. Often, there exists a dynamic coupling
between the rigid and flexible components; which makes the design
of high-performance controllers for such systems very complex.

The nonlinear boundary control law for the nonlinear, hybrid
body-beam model requires the following measurements at the
boundaries of the rotor:

Displacement of the beam,

Shear force experienced by the beam,

Curvature of the beam, and

Time rates of change of the above quantities

While the model-based control law which assume exact knowledge
of the system parameters exhibits exponential regulation, the
asymptotic control law which estimates the system parameters online
exhibits asymptotic regulation